No, but they show an icon in AdWords and Google Products One Box results next to stores that take Checkout. Any trust indicator like that usually helps. It may

No, but they show an icon in AdWords and Google Products One Box results next to stores that take Checkout. Any trust indicator like that usually helps. It may increase your chances of appearing in the One Box as well (as opposed to simply determining whether you get an icon next to your name), but I haven't heard that definitively.